• Home
• About
• Contact
• RSS

Knowing and Teaching Elementary Mathematics

May 8th, 2006 | View Comments

Author: Liping Ma
Publisher: Lawrence Erlbaum Associates
Rating:
Buy Knowing and Teaching Elementary Mathematics on Amazon.com

The full title of this book is Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States.

I first learned of this book as an undergrad, when my research advisor at the time recommended I read it. Although I didn’t quite realize it at the time, reading this book was one of those life-changing moments for me. This book marks the beginning point of my career and shines a guiding beacon down the path I should follow. “This is the state of math education in the United States,” it says, “Do what you can to change it.”

If you follow math education news at all, the nature of Ma’s findings should not surprise you, although some of the specifics might. The math education uninitiated may be shocked and appalled at what she finds. The book contains an implicit indictment of the way elementary math teachers are trained and certified in the United States.

In this book, Ma compares and contrasts math teachers from China and from the United States. As a group, the teachers from China have fewer years of education and fewer secondary degrees. As a group, the teachers from China are much more equipped to teach math to students so they wind up understanding the meaning behind the numbers and symbols, or as Ma puts it, so students acquire a “profound understanding of mathematics.”

The main contrast that Ma draws is that Chinese teachers teach the mathematical relationships between numbers and operators while American teachers teach algorithms to solve problems. The problem is that the algorithms and problems become arbitrary and nearly meaningless when divorced from the underlying mathematical structure. In a number of cases, the American teachers cannot explain themselves why the algorithms are the way they are, beyond “this is how I was taught to do it.”

One striking example of this is how some American teachers in the sample teach long multiplication. As we all know, to perform column multiplication of multi-digit numbers, we work from right to left, multiplying the digits of the lower number with the top number, and successively indent each row as we go. Some American teachers recommend putting zeros or happy faces or stickers in the rightmost columns of each row to serve as “placeholders,” or reminders to indent.

This idea of a “placeholder” is mathematically nonsensical and removes the notion of place value from the problem of long multiplication. When taught this way, students never learn the relationship between columnar long multiplication and its relationship to equations like: 123 x 456 = 123 x (400 + 50 + 6).

This book is definitely required reading for anyone who is entering into math education or a related field. This book is highly recommended reading for parents who are concerned about their children’s math education.

Buy Knowing and Teaching Elementary Mathematics on Amazon.com

Yvonne posted this on May 8th, 2006 @ 12:22pm in Book Reviews, Education, Mathematics | Permalink to "Knowing and Teaching Elementary Mathematics"

2 Comments

Keep track of the discussion! Subscribe to this post's RSS feed.

Have something to say? Leave your own comment!
| Trackback |

Enter search keywords:

| Back to Top |